Universitatea "Babeş-Bolyai" din Cluj-Napoca

Facultatea de Matematică şi Informatică
FISA DISCIPLINEI

Analiză nenetedă

Non-smooth analysis

Cod	Semes- trul	Ore: C+S+L	Credite	Tipul	Sectia
MO033	7	2+2+0	6	optionala	Matematică-Informatică (Mathematics-Computer Science)

Cadre didactice indrumatoare

Teaching Staff in Charge

Prof. Dr. MURESAN Marian, mmarian@math.ubbcluj.ro

Obiective	Aims
Formarea si dezvoltarea abilitatii studentilor de a aborda probleme de optimizare cu date nenetede.	Training up and improving the students' skill to deal with optimization problems with nonsmooth data.

Continut

1. Introducere 1.1. Exemple de probleme de optimizare avand date nederivabile 2.1. Penalitati si restrictii 2. Multifunctii 2.1. Convergente de multimi 2.2. Notiuni de masurabilitate, teoreme de selectie 3. Subgradienti 3.1. Definitii si proprietati de baza 3.2. Legatura cu derivatele si subderivatele 3.2. Reguli de calcul 3.3. Conuri: Clarke, Bouligand, intermediar, Ioffe, Mordukhovich 4. Geometria analizei nenetede 4.1. Principii variationale 4.2. Normale proximale si subgradienti proximali 4.3. Normale proximinale la limita si subgradienti proximali la limita 4.4. Dualitate 5. Calculul subdiferential 5.1. Reguli de calcul 5.2. Regula generalizata a multiplicatorilor lui Lagrange si aplicatii 6. Aplicatii 6.1. Metoda arcului adjunct in optimizarea neneteda 6.2. Aplicatii in economie, puncte de echilibru 6.3. Aplicatii in inginerie

Bibliografie

1. Choset, H., Nonsmooth analysis, convex analysis, and their applications to motion planning, Intern. J. Comp. Geo. Appl., vol. 9(1999), nr. 4-5, 447-467. 2. Clarke, F. H., Optimization and Nonsmooth Analysis, SIAM, Philadelphia, 1990. 3. Jofre, A., A second-welfare theorem in non-convex economies, Canad. Math. J., vol. 27(2000), 175-184. 4. Loewen, P. D., Optimal Control and Nonsmooth Analysis, AMS, Providence, 1993. 5. Loewen, P. D., Rockafellar, T. R., The adjoint arc in nonsmooth optimization, SIAM J. Control Optim., 325(1991), 39-72. 6. Khan, M. A., Ioffe's normal cone and the foundations of welfare economics: the infinite dimensional theory, J. Math. Anal. Appl., vol. 161(1991), 284-298. 7. Mordukhovich, B., The extremal principle and its applications to optimixation and economics, in Optimization and related topics (A. Rubinov and B. Glover, eds.) Applied Optimization, vol. 47, Kluwer, 343-369. 8. Muresan, M., Analiza neneteda, Risoprint, Cluj-Napoca, 2001. 9. Rockafellar, T. R., Wets, R. J.-B., Variational Analysis, Springer, New York, 1998.

Evaluare	Assessment
Un referat si un examen oral.	A review and an exam.